Any fool can know. The point is to understand. – Albert Einstein
2024
Transformation Groups: AIMS South Africa (1st semester)
Group Actions : GGC Seminar at Rhodes University (1st semester)
Topics in Geometry: ERASMUS+ international cooperation project at the University of Palermo (2nd semester)
2023
Some Group Theory : GGC Seminar at Rhodes University (1st semester)
A Little Lie Theory : GGC Seminar at Rhodes University (2nd semester)
Topics in Geometry : ERASMUS+ international cooperation project at the University of Palermo (2nd semester)
Courses
I taught a variety of courses over the years (ranging from first year Calculus to specialized fourth year courses). In the last decade or so, I have taught the following courses:
Discrete Mathematics (first year, 65 lectures) Contents: Propositions and predicates; sets and numbers; functions; mathematical induction; counting; recursion; linear equations and matrices; determinants; vectors, lines, and planes; complex numbers. (COMPLETE lecture notes are available)
Groups and Geometry (second year; 26 lectures) Contents: Geometric transformations; translations and halfturns; reflections and rotations; isometries; symmetry; similarities; affine transformations. (COMPLETE lecture notes are available)
Linear Algebra (second year, 39 lectures) Contents: Linear systems; matrix algebra; determinants; vector spaces; linear transformations; inner product spaces; spectral decomposition.
Linear Control (third year, 39 lectures) Contents: Linear dynamical systems; linear control systems; stability; optimal control. (COMPLETE lecture notes are available)
Naive Lie Theory (fourth year: Hons, 26 lectures) Contents: Geometry of complex numbers and quaternions; groups; generalized rotation groups; the exponential map; the tangent space; structure of Lie algebras; the matrix logarithm; topology; simply connected Lie groups. Textbook: "Naive Lie Theory" by J. Stillwell (Springer, 2008)
Matrix Groups (fourth year: Hons, 26 lectures) Contents: Groups of transformations; actions of groups on sets; Euclidean spaces; matrix groups; the matrix exponential; Lie algebras. (COMPLETE lecture notes are available)
Geometry and Topology (fourth year: Hons, reading course) Contents: Euclidean geometry; spherical and hyperbolic geometry; geometry and group theory; topology. Textbook: "Geometry and Topology" by M. Reid and B. Szendroi (Cambridge Univ Press, 2005)
Lecture Notes
You will find here lecture notes (some incomplete) for the following courses: